arXiv:2607. 01694v1 Announce Type: new Abstract: Solving partial differential equations (PDEs) with high-frequency solutions remains a central challenge in physics-informed machine learning due to spectral bias -- the tendency of neural networks to learn low-frequency components preferentially.
By Xiong Xiong, Ruonan Zhai, Zheng Zeng, Sheng Zhou, Rongchun Hu, Zichen Deng
arXiv:2606. 30930v1 Announce Type: cross Abstract: Modern deep learning has been shown to operate at the edge of stability, routinely using learning rates far larger than those justified by classical optimization theory.
By Konstantinos Emmanouilidis, Lachlan MacDonald, Salma Tarmoun, Rene Vidal
arXiv:2401. 01599v4 Announce Type: replace Abstract: The generalization error curve of certain kernel regression method aims at determining the exact order of generalization error with various source condition, noise level and choice of the regularization parameter rather than the minimax rate.
By Yicheng Li, Weiye Gan, Zuoqiang Shi, Qian Lin
arXiv:2606. 06470v1 Announce Type: new Abstract: We propose a preconditioning (PC) layer, a weight parameterization via polynomial preconditioner that ensures stable weight conditioning throughout LLM training.
By Senmiao Wang, Tiantian Fang, Haoran Zhang, Yushun Zhang, Kunxiang Zhao, Alex Schwing, Ruoyu Sun
arXiv:2606. 10130v1 Announce Type: cross Abstract: Reservoir computers benefit from the inherent complexity of optical phenomena, which provide rich, often nonlinear dynamics.
By Sobhi Saeed, Mehmet M\"uft\"uoglu, Glitta R. Cheeran, Juliane Heim, Bennet Fischer, Mario Chemnitz
arXiv:2511. 19716v3 Announce Type: replace-cross Abstract: Stochastic Gradient Descent (SGD) often slows in the late stage of training due to anisotropic curvature and gradient noise.
By Mitchell Scott, Tianshi Xu, Ziyuan Tang, Alexandra Pichette-Emmons, Qiang Ye, Yousef Saad, Yuanzhe Xi